
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 proposition $p$: The line $x-2y+3=0$ and the parabola $y^{2}=mx(m\neq 0)$ have no intersection points, and proposition $q$: The equation $\dfrac{x^{2}}{5-2m}+\dfrac{y^{2}}{m}=1$ represents a hyperbola. If $p\vee q$ is true, and $p\wedge q$ is false, find the range of the real number $m$.

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