
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
For a bijective function  $g : R \to R$ , we say that a function  $f : R \to R$  is its superinverse if it satisfies the following identity  $(f \circ g)(x) = g^{-1}(x)$ , where  $g^{-1}$  is the inverse of  $g$ . Given  $g(x) = x^3 + 9x^2 + 27x + 81$  and  $f$  is its superinverse, find  $|f(-289)|$ .

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