
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
Two alloys of lead and tin are available. In the first alloy, the mass ratio of lead to tin is $1: 2$; in the second alloy, the mass ratio is $2: 3$. How many grams of the first alloy should be used to obtain 22 grams of a new alloy with a mass ratio of lead to tin of $4: 7$?

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