
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
Given the curve defined by:
\[ f(x) = 
  \begin{cases} 
   x & \text{for } 0 \le x \le 4, \\
   3x - 8 & \text{for } 4 \le x \le 7, \\
   x^2 - 14x + 49 & \text{for } 7 \le x \le 10 
  \end{cases}
\]
find the area bounded by the $x$-axis, the line $x=10$, and the curve.

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