
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 circle \(C\) has radius 1 and touches the line \(L\) at point \(P\). The point \(X\) lies on the circle \(C\) and \(Y\) is the foot of the perpendicular from \(X\) to the line \(L\). Find the maximum possible value of the area of triangle \(PXY\) as \(X\) varies.

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