
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
If two congruent 30-60-90 triangles are placed such that their hypotenuses coincide fully, and one triangle is rotated 30° around the midpoint of the hypotenuse relative to the other, where the hypotenuse of each triangle is 24, find the area common to both triangles.

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