
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
Find all functions  $f: (0, +\infty)\cap\mathbb{Q}\to (0, +\infty)\cap\mathbb{Q}$  satisfying thefollowing conditions:
[list=1]
[*]  $f(ax) \leq (f(x))^a$ , for every  $x\in (0, +\infty)\cap\mathbb{Q}$  and  $a \in (0, 1)\cap\mathbb{Q}$ [*]  $f(x+y) \leq f(x)f(y)$ , for every  $x,y\in (0, +\infty)\cap\mathbb{Q}$ [/list]

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