
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 $f(x)=4\cos \omega x\cdot \sin (\omega x+ \frac{\pi }{6})+a\ (\omega > 0)$, the highest point on the graph has a y-coordinate of $2$, and the distance between two adjacent highest points on the graph is $\pi$.

(1) Find the values of $a$ and $\omega$;

(2) Find the interval(s) where the function $f(x)$ is decreasing on $[0,\pi]$.

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