
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  $x,y,z$  be  positive reals , such that  $x+y+z=1399$  find the
   $$ \max( [x]y + [y]z + [z]x )  $$   
(  $[a]$  is the biggest integer not exceeding  $a$ )

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