
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
Right triangles $T_1$ and $T_2$ have areas of 3 and 4, respectively. A leg of $T_1$ is congruent to a leg of $T_2$, and the hypotenuse of $T_1$ is twice the length of the hypotenuse of $T_2$. Determine the square of the product of the lengths of the other (third) sides of $T_1$ and $T_2$.

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