
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
Given two functions:
$$\begin{array}{ccc}
f(x) & = & 2x^3 - 5x^2 + 3x + 7\\
g(x) & = & 3x^3 - kx^2 + 4
\end{array}$$
If \( f(5) - g(5) = 45 \), find the value of \( k \).

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