
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
For positive real nubers  $a,b,c$  find the maximum real number  $x$ , such that there exist positive numbers  $p,q,r$ , such that  $p+q+r=1$  and  $x$  does not exceed numbers  $a\frac{p}{q}, b\frac{q}{r}, c\frac{r}{p}$  

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