
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
The area formed by all points L within a triangle JKL is less than or equal to 10, where J(2, 7), K(5, 3), and L(r, t), with constraints 0 ≤ r ≤ 10 and 0 ≤ t ≤ 10, can be described as a region R. Express the area of R as a fraction in lowest terms, equal to (300 + a)/(40 - b) for some positive integers a and b. Find a + b.

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