
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
Determine the nonnegative integers a, b, and c for the function:
\[ 
f(x) = \left\{
\begin{array}{cl}
ax+2 & \text{if } x > 0, \\
4b & \text{if } x = 0, \\
2bx+c & \text{if } x < 0.
\end{array}
\right. 
\]
given that \(f(1)=3\), \(f(0)=8\), and \(f(-1)=-4\).

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