
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
Solve the equation \( f^{-1}(g(x)) = h(x) \), where \( f^{-1}(x) \) is the inverse function of \( f(x) \), given that \( f(x) = x^{3} + 2x^{2} + 3x + 4 \), \( g(x) = x^{4} + 2x^{3} + x^{2} + 11x + 11 \), and \( h(x) = x + 1 \).

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