
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 a first-degree function $f(x) = (m^2 - 1)x + m^2 - 3m + 2$, if $f(x)$ is a decreasing function and $f(1) = 0$.
1. Find the value of $m$;
2. If $f(x+1) \geq x^2$, find the range of $x$.

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