
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-   $$ x! + 2^y =(x+1)! $$  Note:  $x!=x \cdot (x-1)!$  and  $0!=1$ . For example,  $5! = 5\times 4\times 3\times 2\times 1 = 120$ .

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