
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 possible non-negative integer solution ( $x,$   $y$ ) of the following equation-   $$ x!+2^y=z! $$  Note:  $x!=x\cdot(x-1)!$  and  $0!=1$ . For example,  $5!=5\times4\times3\times2\times1=120$ .

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