
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 $f(x)=\sin (x+θ)+a\cos (x+2θ)$, where $a\in R$, $θ\in(-\frac{π}{2}, \frac{π}{2})$
(1) When $a=\sqrt {2}$, $θ=\frac{π}{4}$, find the maximum and minimum values of $f(x)$ on the interval $[0,π]$;
(2) If $f(\frac{π}{2})=0$, $f(π)=1$, find the values of $a$ and $θ$.

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