
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 $f(\alpha) = \frac{\sin(\pi - \alpha)\cos(2\pi - \alpha)\tan(\alpha - \pi)}{\tan(-\alpha - \pi)\cos(\frac{\pi}{2} - \alpha)}$,

(1) Simplify $f(\alpha)$;

(2) If $\alpha$ is an angle in the first quadrant and $f(\alpha) + \sin\alpha = \frac{2}{3}$, find the value of $\sin\alpha + \cos\alpha$.

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