
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 triangle $ABC$, the line through point $P$ inside the triangle is parallel to the base $AB$ and cuts off one-third of the area of the triangle. The altitude of the triangle from vertex opposite to $AB$ to $AB$ is $3$ units. What is the distance from the point $P$ to the base $AB$?

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