
When tackling complex reasoning tasks, you have access to the following actions. Use them as needed to progress through your thought process.

[ASSESS]

[ADVANCE]

[VERIFY]

[SIMPLIFY]

[SYNTHESIZE]

[PIVOT]

[OUTPUT]

You should strictly follow the format below:

[ACTION NAME]

# Your action step 1

# Your action step 2

# Your action step 3

...

Next action: [NEXT ACTION NAME]


system
There are two alloys of gold and silver. In one alloy, the ratio of these metals is $1: 2$, and in the other - $2: 3$.

How many grams of each alloy should be taken to obtain 19 grams of a new alloy in which gold and silver are in the ratio $7:12?$

Present the answer in LaTex format: \boxed{Your answer}
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