
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 \( g(x) = |x - 5| + |x - 7| - |2x - 12| + |3x - 21| \) for \( 5 \leq x \leq 10 \). Find the sum of the largest and smallest values of \( g(x) \).
**A)** 9
**B)** 10
**C)** 11
**D)** 12

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