
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 $A$ be the area enclosed by the $x$-axis, the line $x=10$, and the curve defined by
\[
g = \left\{ (x, y) \mid y = 2x \text{ for } 0 \le x \le 6, \; y = 3x - 6 \text{ for } 6 \le x \le 8, \; y = x + 6 \text{ for } 8 \le x \le 10 \right\}.
\]
Determine the value of $A$.
A) 126
B) 132
C) 138
D) 144

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