
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
Let  $ABCD$  be a square of side length  $1$ , and let  $E$  and  $F$  be points on  $BC$  and  $DC$  such that  $\angle{EAF}=30^\circ$  and  $CE=CF$ . Determine the length of  $BD$ .

*2015 CCA Math Bonanza Lightning Round #4.2*

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