
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
Consider the given functions:
$$\begin{array}{ccc}
f(x) & = & 5x^3 - \frac{1}{x} + 3\\
g(x) & = & x^2 - kx + c
\end{array}$$
If $f(2) - g(2) = 2$, what are the values of $k$ and $c$ assuming $k=1$?

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