
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
 $ABC$  is an isosceles triangle with  $AB=AC$ . Point  $D$  is constructed on AB such that  $\angle{BCD}=15^\circ$ . Given that  $BC=\sqrt{6}$  and  $AD=1$ , find the length of  $CD$ .

*2018 CCA Math Bonanza Lightning Round #4.3*

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