
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 \[f(x) =
\begin{cases}
5x + 20 &\text{if } x < 3, \\
3x - 15 &\text{if } x \geq 3.
\end{cases}
\]
Find the sum of all possible values of \(x\) for which \(f(x) = 0\).

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