
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 $f(x) = (2 - a)(x - 1) - 2\ln{x}$ (where $a \in \mathbb{R}$).
1. Find the monotonic intervals of $f(x)$ when $a = 1$.
2. Determine the range of values for $a$ such that the function $f(x)$ has no zero points in the interval $\left(0, \frac{1}{3}\right)$.

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