
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 sides $a$, $b$, and $c$ opposite to angles $A$, $B$, and $C$, respectively. It is known that $c=3$ and $\sin (C- \frac {\pi}{6}) \cdot \cos C = \frac {1}{4}$.

1. Find the measure of angle $C$.
2. If vectors $\overrightarrow{m} = (1, \sin A)$ and $\overrightarrow{n} = (2, \sin B)$ are collinear, find the values of $a$ and $b$.

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