
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 $p$: For any $x \in \mathbb{R}$, $x^2 + 1 > m$, and proposition $q$: The linear function $f(x) = (2 - m)x + 1$ is an increasing function.

$(1)$ Write the negation of proposition $p$;  
$(2)$ If the proposition "$p \lor q$" is true, and "$p \land q$" is false, find the range of the real number $m$.

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