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PRECIOUS-Gold claws way back into the black after Trump sacks Tillerson

* Spot gold to fall further towards $1,300/oz - analyst

* Trump fires secretary of state Tillerson

(Adds Trump news, U.S. data, updates prices) LONDON, March 13 (Reuters) - Gold bounced into positive territory on Tuesday as the dollar lost ground following news that U.S. President Donald Trump has replaced Secretary of State Rex Tillerson, and after U.S. inflation data in line with forecasts.

Spot gold was up 0.2 percent at $1,325.09 per ounce

gained 0.4 percent to $1,325.70 an ounce. Trump on Tuesday said he has replaced Tillerson with Central Intelligence Agency Director Mike Pompeo and has tapped Gina Haspel to lead the CIA, in the biggest shake up of his cabinet so far.

The dollar index gave up its gains and fell 0.17

percent to 89.742, making commodities priced in the greenback cheaper for buyers using other currencies. Also weighing on the dollar was news that U.S. consumer prices cooled in February, the latest indication that an anticipated pickup in inflation probably will be only gradual. Some investors had been worried that a stronger than expected CPI reading could stoke expectations that the Federal Reserve will raise interest rates four times rather than three this year. Georgette Boele, commodity strategist at ABN AMRO in Amsterdam, said gold was vulnerable after it had failed three times to rally since touching a 1-1/2 year peak of $1,342.70 on Jan. 25. "Overall the outlook is not looking that great in the short term. I still expect prices to go towards $1,300."

In other precious metals, silver rose 0.7 percent to

$16.60 per ounce. Net long positions in U.S. silver futures increased for the first time since January, UBS analyst Joni Teves said in a note. "Silver has been such an underperformer of late and one of the few positive factors currently is that net length is very lean. Despite recent gains, net speculative positions in silver are still only 18 percent of the record."

Platinum rose 0.6 percent to $968 an ounce, while palladium gained 1 percent to $988 per ounce.

ING analyst Oliver Nugent said in a note that the platinum price will struggle to move back above palladium. "Based on our own forecasts, we dont think such a move will happen for the next few years due to platinum's weaker fundamentals with the palladium backwardation actually making it more expensive for investors to short the ratio." The platinum/palladium ratio was at 0.978, up from 0.943 in late February and 0.85 in mid-December. Palladium flipped to a premium over platinum last September for the first time since 2001.

(Additional reporting by Nithin Prasad and Eileen Soreng in Bengaluru Editing by Mark Potter)