
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
Let  $\mathcal{F}$  be the set of all functions  $f : (0,\infty)\to (0,\infty)$  such that  $f(3x) \geq f( f(2x) )+x$  for all  $x$ . Find the largest  $A$  such that  $f(x) \geq A x$  for all  $f\in\mathcal{F}$  and all  $x$ .

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