
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 \( g(x) = |x-5| + |x-3| - |3x-15| \) for \( 3 \leq x \leq 10 \). Find the sum of the largest and smallest values of \( g(x) \).
**A)** \(-5\)
**B)** \(-4\)
**C)** \(-3\)
**D)** \(-2\)
**E)** \(0\)

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