
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
In unit square \(ABCD\), points \(E, F, G\) are chosen on sides \(BC, CD,\) and \(DA\) respectively such that \(AE\) is perpendicular to \(EF\) and \(EF\) is perpendicular to \(FG\). Given that \(GA = \frac{404}{1331}\), find all possible values of the length of \(BE\).

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