
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 that the area of an equilateral triangle $ABC$ is 1, and $P$ is a point inside $\triangle ABC$, with the areas of $\triangle PAB$, $\triangle PBC$, and $\triangle PCA$ being equal, then the total number of points $P$ that satisfy the condition is $\boxed{1}$; the area of $\triangle PAB$ is $\boxed{\frac{1}{3}}$.

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