
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 \[f(x) = \left\{
\begin{array}{cl}
2ax+4 & \text{ if }x>0, \\
a+b & \text{ if }x=0, \\
3bx+2c & \text{ if }x<0.
\end{array}
\right.\]If $f(1)=6$, $f(0)=7$, and $f(-1)=-4$, and $a$, $b$, and $c$ are integers, then what is $a+b+c$?

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