
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 statements $p$: The line $mx - y + 1 = 0$ intersects the circle $(x - 2)^2 + y^2 = 4$; and $q$: The real number $m$ satisfies the equation $\frac{x^2}{m - 1} + \frac{y^2}{2 - m} = 1$ representing a hyperbola.

1. Find the range of values for the real number $m$ if the statement "$p \land q$" is true.
2. Find the range of values for the real number $m$ if the statement "$p \land q$" is false and "$p \lor q$" is true.

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