
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 a triangle where $B$ is twice the measure of $A$, i.e., $B = 2A$. After drawing an altitude from the vertex $C$ to the base $AB$ which divides $C$ into $C_1$ and $C_2$, where $C_2$ is adjacent to side $a$, find the relationship between $C_1$, $C_2$, and the angle $A$.
A) $C_1 - C_2 = A$
B) $C_1 - C_2 = 2A$
C) $C_1 + C_2 = 3A$
D) $C_1 - C_2 = 3A$
E) $C_1 + C_2 = A$

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