
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 $f(x) = \sqrt{2}\cos \left(x- \frac{\pi}{12}\right)$, where $x \in \mathbb{R}$.

(1) Find the value of $f\left(\frac{\pi}{3}\right)$;

(2) If $\cos \theta= \frac{3}{5}$, where $\theta \in \left(\frac{3\pi}{2},2\pi\right)$, find $f\left(\theta- \frac{\pi}{6}\right)$.

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