
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
Let  $\otimes$  be a binary operation that takes two positive real numbers and returns a positive real number.  Suppose further that  $\otimes$  is continuous, commutative  $(a\otimes b=b\otimes a)$ , distributive across multiplication  $(a\otimes(bc)=(a\otimes b)(a\otimes c))$ , and that  $2\otimes 2=4$ .  Solve the equation  $x\otimes y=x$  for  $y$  in terms of  $x$  for  $x>1$ .

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