
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 non-negative integers  $ x,y,z$  such that  $ 5^x \plus{} 7^y \equal{} 2^z$ .
 :lol: 
(*Daniel Kohen, University of Buenos Aires - Buenos Aires,Argentina*)

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