
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
\[f(x) =
\begin{cases} 
x/2 & \text{when } 0 \le x \le 6, \\
3x - 13 & \text{when } 6 \le x \le 10.
\end{cases}\]
Calculate the area $A$.
A) 50
B) 53
C) 61
D) 73

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