
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
Circle \(\omega\) is inscribed in rhombus \(H M_{1} M_{2} T\) so that \(\omega\) is tangent to \(\overline{H M_{1}}\) at \(A\), \(\overline{M_{1} M_{2}}\) at \(I\), \(\overline{M_{2} T}\) at \(M\), and \(\overline{T H}\) at \(E\). Given that the area of \(H M_{1} M_{2} T\) is 1440 and the area of \(E M T\) is 405, find the area of \(A I M E\).

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