
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 $f(x)=a(2\cos ^{2} \frac {x}{2}+\sin x)+b$.
(1) When $a=1$, find the monotonically increasing interval and the equation of the symmetry axis of $f(x)$;
(2) When $a > 0$ and $x\in[0,\pi]$, the range of $f(x)$ is $[3,4]$, find the values of $a$ and $b$.

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