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

(1) Find the value of $f(\frac{5π}{4})$;

(2) Let $\alpha, \beta \in [0, \frac{π}{2}], f(3\alpha + \frac{π}{2}) = \frac{10}{13}, f(3\beta + 2π) = \frac{6}{5}$, find the value of $\cos(\alpha + \beta)$.

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