
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 $f(x) = \ln(x+1) + ax^2 - x$ where $a \in \mathbb{R}$.
1. When $a = \frac{1}{4}$, find the monotonic intervals of the function $y = f(x)$.
2. If for any real number $b \in (1,2)$, the maximum value of the function $f(x)$ when $x \in (-1,b]$ is $f(b)$, find the range of values for $a$.

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