
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 \[f(x) = \left\{
\begin{array}{cl}
x^2 - 4x + 4 &\text{ if } x \geq 6, \\
-x^2 + 3x + 4 &\text{ if } 0 < x < 6, \\
4x + 8 &\text{ if } x \leq 0.
\end{array}
\right.\] Find $f(-5) + f(3) + f(8)$.

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