
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 two statements $q$ and $p$:
$q$: For any real number $x$, the inequality $x^{2}-2x+m\geqslant 0$ always holds;
$q$: The equation $\frac{x^{2}}{m-3}-\frac{y^{2}}{m}=1$ represents a hyperbola with foci on the $x$-axis.

1. If statement $q$ is true, find the range of values for the real number $m$.
2. If the statement "$p\vee q$" is true and "$p\wedge q$" is false, find the range of values for the real number $m$.

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