
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
Given a right triangle \( \triangle A B C \) with \( A \) as the right-angle vertex and \( \angle B = 60^\circ \), \( A D \perp B C \), and \( A E \) bisects \( \angle B A C \). If \( A B = a \), calculate the length of \( D E \).

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