
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 propositions $p: \exists x_0 \in \mathbb{R}, \text{ such that } x_0 + \frac{1}{3}m = e^{x_0} \ (e \text{ is the base of the natural logarithm})$ and $q:\text{The eccentricity of the ellipse } \frac{x^2}{m} + \frac{y^2}{5} = 1 \text{ is in the range } \left( \frac{1}{2}, \frac{2}{3}\right)$, if the proposition $(\neg p) \vee (\neg q)$ is false, find the range of values for the real number $m$.

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