
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 triangle $\triangle ABC$, angle $A$ is twice angle $B$, and the side opposite to angle $B$ is $b$. An altitude dropped from vertex $C$ to base $AB$ divides angle $C$ into two parts, $C_1$ by angle $A$ and $C_2$ by angle $B$. Given that $ABC$ is isosceles with $AB = AC$, find the exact values of $C_1$ and $C_2$.
A) $C_1 = 90^\circ - 1.5B, C_2 = 1.5B$
B) $C_1 = 90^\circ, C_2 = 90^\circ$
C) $C_1 = 2B, C_2 = 90^\circ - 2B$
D) $C_1 = 90^\circ - 1.5B, C_2 = 90^\circ - 1.5B$
E) $C_1 = 3B, C_2 = 180^\circ - 3B$

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