
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 that the vertex of angle $\alpha$ coincides with the origin $O$, its initial side coincides with the non-negative semi-axis of the $x$-axis, and its terminal side passes through point $P(-\frac{3}{5}, -\frac{4}{5})$.

(1) Find the value of $\sin(\alpha + \pi)$;

(2) If angle $\beta$ satisfies $\sin(\alpha + \beta) = \frac{5}{13}$, find the value of $\cos(\beta)$.

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