
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 functions: 
$$
\begin{array}{ccc}
f(x) & = & 7x^3 - \frac{1}{x} + 5\\
g(x) & = & x^3 - k
\end{array}
$$
Find the value of $k$ if $f(3) - g(3) = 5$.

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