
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 system of inequalities
$$\begin{cases}
x - 2y + 5 \geq 0, \\
3 - x \geq 0, \\
x + y \geq 0,
\end{cases}$$
find the range of values for the real number $m$ such that the set of points $(x, y)$ satisfying the above system is a subset of the set $\{(x, y) \ | \ x^2 + y^2 \leq m^2 \}$, where $m > 0$.

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