
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  $ X$  be the set of all positive integers greater than or equal to  $ 8$  and let  $ f: X\rightarrow X$  be a function such that  $ f(x\plus{}y)\equal{}f(xy)$  for all  $ x\ge 4, y\ge 4 .$  if  $ f(8)\equal{}9$ , determine  $ f(9) .$ 

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