
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  $L_1$  and  $L_2$  be perpendicular lines, and let  $F$  be a point at a distance  $18$  from line  $L_1$  and a distance  $25$  from line  $L_2$ . There are two distinct points,  $P$  and  $Q$ , that are each equidistant from  $F$ , from line  $L_1$ , and from line  $L_2$ . Find the area of  $\triangle{FPQ}$ .

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