
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
Point P is inside $\triangle ABC$, and it satisfies the condition $\overrightarrow{AP} + 2\overrightarrow{BP} + 3\overrightarrow{CP} = \overrightarrow{0}$. Let Q be the point where the extension line of $\overrightarrow{CP}$ intersects with AB. Let $\overrightarrow{CP} = p$, express $\overrightarrow{CQ}$ in terms of $p$.

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