
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 an isosceles triangle $\triangle ABC$, base angles $A$ and $B$ are such that $A = B$. Let's say $A = 30^\circ$. The altitude from vertex $C$ to the base $AB$ divides the angle $C$ into two parts $C_1$ and $C_2$, with $C_2$ adjacent to side $a$. Calculate $C_1 - C_2$.

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