
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 a point $A(x_{A},y_{A})$ on the unit circle (with the center at the origin $O$ and a radius of $1$), rotate ray $OA$ counterclockwise by $\frac{π}{3}$ to $OB$, intersecting the unit circle at point $B(x_{B},y_{B})$. It is known that $m > 0$. If the maximum value of $my_{A}-2y_{B}$ is $\sqrt{7}$, find the real number $m$.

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