
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
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Let \[f(x) = \left\{
\begin{array}{cl}
ax+4 & \text{ if }x>0, \\
ab & \text{ if }x=0, \\
bx+c & \text{ if }x<0.
\end{array}
\right.\]If \( f(3)=7 \), \( f(0)=6 \), and \( f(-3)=-15 \), and \( a \), \( b \), and \( c \) are nonnegative integers, then what is \( a+b+c \)?

**

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