
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 $\triangle ABC$ be an isosceles triangle where $AB = AC$, and $B$ is a constant angle at $50^\circ$. A line through vertex $C$ and perpendicular to $AB$ intersects the line extended from side $AB$ at point $D$. Let $\angle ACD = x$. The part of $\angle ACB$, which is $180^\circ - x$, is divided into two parts $C_1$ and $C_2$ with $C_2$ adjacent to side $AB$. Determine $\angle C_1 - \angle C_2$.
A) $x - 80^\circ$
B) $2x - 80^\circ$
C) $180^\circ - 2x$
D) $80^\circ - 2x$
E) $80^\circ + 2x$

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