
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
Assume triangle $\triangle ABC$ has one angle $A$ that is $15^\circ$ smaller than another angle $B$. An altitude from angle $C$ bisects $C$ into two angles $C_1$ and $C_2$, with $C_2$ adjacent to the side opposite $B$. Determine the relationship between $C_1 - C_2$ and $A - B$.
A) $15^\circ$
B) $30^\circ$
C) $45^\circ$
D) $60^\circ$

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