
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
Given a triangle $\triangle ABC$, where the lengths of the sides opposite to angles $A$, $B$, and $C$ are $a$, $b$, and $c$ respectively. It is known that vector $\overrightarrow{m} = (\sin A + \sin C, \sin B - \sin A)$ and vector $\overrightarrow{n} = (\sin A - \sin C, \sin B)$ are orthogonal.

1. Find the measure of angle $C$.
2. If $a^2 = b^2 + \frac{1}{2}c^2$, find the value of $\sin(A - B)$.

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