
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 $f(x)=Asin({ωx+\frac{π}{6}})({A＞0,ω＞0})$ satisfies any two of the following conditions:<br/>① The maximum value of the function $f\left(x\right)$ is $2$;<br/>② The distance between two adjacent axes of symmetry of the graph of $f\left(x\right)$ is $\frac{π}{2}$.<br/>$(1)$ Find the analytical expression of $f\left(x\right)$;<br/>$(2)$ Find the sum of all solutions of the equation $f\left(x\right)+1=0$ on the interval $\left[-\pi ,\pi \right]$.

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