
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
Suppose that for two real numbers  $x$  and  $y$  the following equality is true:  $$ (x+ \sqrt{1+ x^2})(y+\sqrt{1+y^2})=1 $$  Find (with proof) the value of  $x+y$ .

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