
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 $\triangle ABC$ with angles $A$, $B$, $C$ and their corresponding opposite sides $a$, $b$, $c$. It is known that $a^{2}+b^{2}-c^{2}=4S_{\triangle ABC}$.

1. Find the measure of angle $C$.
2. If $c=\sqrt{2}$, find the range of values for $a-\frac{\sqrt{2}}{2}b$.

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