
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
Here are two functions:
$$
\begin{array}{ccc}
f(x) & = & 4x^3 - 3x^2 + 2x + 5 \\
g(x) & = & x^3 - (k+1)x^2 - 7x - 8
\end{array}
$$
If \( f(5) - g(5) = 24 \), what is the value of \( k \)?

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