
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
The full score for this question is 10 points.  
Given the function $f(x) = x^2 + 2x + a\ln x$.  
(1) If $f(x)$ is a monotonic function on the interval $(0,1)$, find the range of values for $a$;  
(2) If for all $t \geq 1$, $f(2t - 1) \geq 2f(t) - 3$, find the range of values for $a$.

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