
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
Let $f(x) = \cos(x + \theta) + \sqrt{2}\sin(x + \phi)$ be an even function, where $\theta$ and $\phi$ are acute angles, and $\cos\theta = \frac{\sqrt{6}}{3}\sin\phi$. Then, evaluate the value of $\theta + \phi$.

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