
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 function $f(x) = m \ln x - x^2 + 2 (m \leqslant 8)$.

(1) Find the monotonic interval of the function $f(x)$ when the slope of the tangent line at the point $(1, f(1))$ is greater than $-2$.

(2) Find the range of $m$ if $f(x) - f'(x) \leqslant 4x - 3$ holds true for $x \in [1, +\infty)$ (Hint: $\ln 2 \approx 0.7$).

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