
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 $f(x)= \sqrt {2}\cos (x- \frac {\pi }{12}),x\in \mathbb{R}$.  
$(1)$ Find the value of $f( \frac {\pi }{3})$;  
$(2)$ If $\cos \theta = \frac {3}{5},\theta \in ( \frac {3\pi }{2},2\pi )$, find $f(\theta - \frac {\pi }{6})$.

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