
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 function $f(x) = (a + 2\cos^{2}x)\cos(2x + \theta)$ is an odd function, and $f(\frac{\pi}{4}) = 0$, where $a \in R$, $\theta \in (0, \pi)$.
(1) Find the values of $a$ and $\theta$;
(2) If $f(\frac{\alpha}{4}) = -\frac{2}{5}$, $\alpha \in (\frac{\pi}{2}, \pi)$, find the value of $\sin(\alpha + \frac{\pi}{3})$.

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