
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
Pentagon \( JAMES \) is such that \( AM = SJ \) and the internal angles satisfy \( \angle J = \angle A = \angle E = 90^\circ \), and \( \angle M = \angle S \). Given that there exists a diagonal of \( JAMES \) that bisects its area, find the ratio of the shortest side of \( JAMES \) to the longest side of \( JAMES \).

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