
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
Let $\triangle ABC$ be an isosceles triangle where $AB$ is the base. An altitude from vertex $C$ to base $AB$ measures 6 units. A line drawn through a point $P$ inside the triangle, parallel to the base $AB$, divides the triangle into two regions of equal area. The vertex angle at $C$ is a right angle. Find the distance from $P$ to $AB$.
- **A)** 1.5
- **B)** 3
- **C)** 4.5
- **D)** 6

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