
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 a triangle  $ABC$  with  $ \angle A = 36^o$  and  $AB = AC$ , the bisector of the angle at  $C$  meets the oposite side at  $D$ . Compute the angles of  $\triangle BCD$ . Express the length of side  $BC$  in terms of the length  $b$  of side  $AC$  without using trigonometric functions.

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