
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 $g(x) = |x-3| + |x-5| - |2x-10| + |x-1|$ for $1 \leq x \leq 9$. Find the sum of the largest and smallest values of $g(x)$.
**A)** 0 
**B)** 1 
**C)** 2 
**D)** 3 
**E)** 4

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