
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 $f(x) = ax^2 - \ln{x}$, where $a \in \mathbb{R}$:

1. If $a = 1$, find the equation of the tangent line to the curve $y = f(x)$ at the point $(1, f(1))$.
2. If $|f(x)| \geq 1$ holds true for all $x \in (0, 1]$, find the range of possible values for $a$.

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