
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
To each pair of nonzero real numbers  $a$  and  $b$  a real number  $a*b$  is assigned so that  $a*(b*c) = (a*b)c$  and  $a*a = 1$  for all  $a,b,c$ . Solve the equation  $x*36 = 216$ .

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