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

(1) Find the values of $a$ and $ω$;

(2) Find the interval where the function $f(x)$ is monotonically decreasing on $[0,π]$.

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