
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
In the given triangle $ABC$, construct the points $C_{1}$ on side $AB$ and $A_{1}$ on side $BC$ such that the intersection point $P$ of lines $AA_{1}$ and $CC_{1}$ satisfies $AP / PA_{1} = 3 / 2$ and $CP / PC_{1} = 2 / 1$. In what ratio does point $C_{1}$ divide side $AB$?

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