
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
Given a triangle $\triangle ABC$ with a base $AB$ and an altitude from vertex $C$ to base $AB$ of length 3, find the distance from point $P$ to the base $AB$ such that a line parallel to $AB$ passing through $P$ divides the triangle into two regions, with the area below the line (including point $P$) being one-third the total area of the triangle.

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