
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 $ƒ(x)=(a+ 2\cos ^{2}x)\cos (2x+θ)$ is an odd function, and $ƒ(\frac{π}{4})= 0$, where $a∈ R$, $θ∈ (0,π)$.

(1) Find the values of $a$ and $θ$;

(2) Let $g(x)= ƒ(x)+ ƒ(x+ \frac{π}{3})$, $x∈ [0, \frac{π}{4}]$, find the maximum and minimum values of $g(x)$, and find the corresponding values of $x$.

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