
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 triangle \( \triangle ABC \), it is given that \( \angle C=90^\circ \), \( \angle A=60^\circ \), and \( AC=1 \). Points \( D \) and \( E \) are on sides \( BC \) and \( AB \) respectively such that triangle \( \triangle ADE \) is an isosceles right triangle with \( \angle ADE=90^\circ \). Find the length of \( BE \).

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