
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 that point $P$ is any point on the graph of the function $f(x) = \ln x$, and point $Q$ is any point on the circle $[x - (e + \frac{1}{e})]^2 + y^2 = \frac{1}{4}$, determine the minimum length of the line segment $PQ$.

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