
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 that $A(x_A, y_A)$ is a point on the unit circle (with the center at the origin $O$ and radius of 1), when the ray $OA$ is rotated counterclockwise by $\frac{\pi}{6}$ to $OB$ intersecting the unit circle at point $B(x_B, y_B)$, and given $m > 0$, if the maximum value of $my_A - 2y_B$ is 2, then the value of the real number $m$ is \_\_\_\_\_\_.

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