
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
Let the function $f(x) = x(e^x-1) - ax^2$ have a tangent line at point $(1, f(1))$ with slope $2e-2$.  
(1) Find the value of $a$;  
(2) If the function $y = f(x)$ is increasing in the interval $(2m-3, 3m-2)$, find the range of the real number $m$.

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