
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
Triangle $ABC$ has an altitude from vertex $C$ to the base $AB$ with a length of 2 units. A line through a point $P$ inside the triangle, parallel to $AB$, divides the triangle such that the area of the smaller part (above the line) to the larger part (below the line) is in the ratio 1:3. What is the distance from $P$ to $AB$?
A) $2$
B) $\sqrt{2}$
C) $1$
D) $2 - \sqrt{2}$
E) $-1 + \sqrt{3}$

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