
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
Consider two piecewise linear functions \( f(x) \) and \( g(x) \). The function \( f(x) \) consists of three segments:
1. \( f(x) = 3x \) from \( x = -3 \) to \( x = -1 \),
2. \( f(x) = -2x + 1 \) from \( x = -1 \) to \( x = 1 \),
3. \( f(x) = 3x - 2 \) from \( x = 1 \) to \( x = 3 \).

The function \( g(x) \) is defined as \( g(x) = 5 - x \) for \( x \) from \( -3 \) to \( 3 \).

Find the sum of all x-coordinates where \( f(x) = g(x) \).

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