
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 $f(x)=2a\sin ωx\cos ωx+2 \sqrt {3}\cos ^{2}ωx- \sqrt {3}(a > 0,ω > 0)$ with a maximum value of $2$ and a smallest positive period of $π$.
$(1)$ Find the analytical expression of the function $f(x)$ and the equation of the axis of symmetry;
$(2)$ Find the interval where the function $f(x)$ is monotonically increasing.

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