
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 the function $f(x)=\sin (2x- \frac {\pi}{6}).$  
$(1)$ Find the period of the function $f(x);$  
$(2)$ In $\triangle ABC,$ if $f(A)=1$ and it satisfies $\sin ^{2}B+ \sqrt {2}\sin A\cdot\sin C=\sin ^{2}A+\sin ^{2}C,$ find the angle $C.$

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