
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 $f(x)=2\sin \left(\frac{1}{3}x-\frac{\pi }{6}\right)$, where $x\in \mathbb{R}$,

    (1) Find $f\left(\frac{5\pi }{4}\right)$;

    (2) Let $\alpha ,\beta \in \left[0,\frac{\pi }{2}\right]$, and $f(3\alpha +\frac{\pi }{2})=\frac{10}{13}$, $f(3\beta +2\pi )=\frac{6}{5}$, find $\cos (\alpha +\beta )$.

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