
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 $f(x)=Asin(ωx+φ)({|φ|＜\frac{π}{2}})$ satisfies three out of the following four conditions:<br/>①$f({\frac{π}{6}})=1$;<br/>②The graph of $f(x)=Asin(ωx+φ)({|φ|＜\frac{π}{2}})$ can be obtained by translating the graph of $y=\sin x-\cos x$;<br/>③The distance between adjacent two symmetry axes is $\frac{π}{2}$;<br/>④The maximum value is $2$.<br/>$(1)$ Identify the three conditions and explain the reasons;<br/>$(2)$ If the symmetry axis of the curve $y=f\left(x\right)$ falls only once in the interval $\left[0,m\right]$, find the range of values for $m$.

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