
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
If point $P$ is located on the plane region defined by the system of inequalities $\begin{cases} x - y + 2 \geqslant 0 \\ x + y - 2 \leqslant 0 \\ 2y \geqslant x + 2 \end{cases}$ and also on the curve defined by the equation $\frac{x^2}{4} + y^2 = m^2$ $(m > 0)$, then the minimum value of $m$ is $(\ \ \ )$.

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