
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 $f(x) =x^2 + (2m-1)x - m\ln x$.
1. When $m=1$, find the extreme values of the curve $y=f(x)$.
2. Determine the monotonic intervals of the function $f(x)$.
3. If for any $m \in (2, 3)$ and $x \in [1, 3]$, it is always true that $mt - f(x) < 1$, find the range of values for the real number $t$.

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