
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
The side of the base \(ABC\) of the regular pyramid \(PABC\) is \(a\), and the lateral edge is \(b\). At what distance from the line \(BC\) should a section of the pyramid be made, parallel to the edges \(BC\) and \(PA\), so that its area is the largest possible?

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