
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
Right triangle  $ABC$  has right angle at  $C$  and  $\angle BAC=\theta$ ; the point  $D$  is chosen on  $AB$  so that  $|AC|=|AD|=1$ ; the point  $E$  is chosen on  $BC$  so that  $\angle CDE=\theta$ .  The perpendicular to  $BC$  at  $E$  meets  $AB$  at  $F$ .  Evaluate  $\lim_{\theta\to 0}|EF|$ .

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