
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
Two congruent 30-60-90 triangles are placed such that one triangle is translated 2 units vertically upwards, while their hypotenuses originally coincide when not translated. The hypotenuse of each triangle is 10. Calculate the area common to both triangles when one is translated.

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