
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
A line in the plane is called strange if it passes through \((a, 0)\) and \((0, 10-a)\) for some \(a\) in the interval \([0,10]\). A point in the plane is called charming if it lies in the first quadrant and also lies below some strange line. What is the area of the set of all charming points?

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