
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 $f(x)=2\cos ^{2}ωx+2 \sqrt {3}\sin ωx\cos ωx+m$, where $ω > 0$, and $m\in\mathbb{R}$. The graph of the function $f(x)$ has its first highest point on the right side of the $y$-axis at $x=\frac{π}{6}$, and it passes through the point $(0,2)$.
1. Find the analytical expression of the function $f(x)$.
2. If $f(x_{0})= \frac{11}{5}$, and $x_{0}\in[\frac{π}{4}, \frac{π}{2}]$, find the value of $\cos 2x_{0}$.

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