
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 functions $f(x)=\ln x+ \frac{1}{x}$ and $g(x)=x+ \frac{1}{x-a}$, if for every $x_1 \in (0,2]$, there exists an $x_2 \in (a,+\infty)$ such that $f(x_1) \geqslant g(x_2)$, then the range of the real number $a$ is

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