
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
If  $X=1+x+x^2+x^3+\cdots$  and  $Y=1+y+y^2+y^3+\cdots$ , what is  $1+xy+x^2y^2+x^3y^3+\cdots$  in terms of  $X$  and  $Y$  only?

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