
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
Let $u$, $f$, and $g$ be functions defined for all real numbers $x$, and satisfy the conditions

\[
\frac{u(x+1)+u(x-1)}{2}=f(x),
\]
\[
\frac{u(x+4)+u(x-4)}{2}=g(x),
\]

express $u(x)$ in terms of $f$ and $g$.

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