
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  $f\colon \mathbb{Q}\to \mathbb{R}_{\geq 0}$  such that for any two rational numbers  $x$  and  $y$  the following conditions hold


- $f(x+y)\leq f(x)+f(y)$ ,
- $f(xy)=f(x)f(y)$ ,
- $f(2)=1/2$ .


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