
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
In triangle $ABC$, three smaller isosceles triangles $PAB$, $QBC$, and $RCA$ are cut off, with $PA=AB=PB$, $QB=BC=QC$, and $RC=CA=RA$. The remaining central area is a regular hexagon. If the total area cut off is $150 \text{ cm}^2$, what is the side length of the regular hexagon?

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