
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
In a college basketball game between the Eagles and Panthers, the game was tied at the end of the first quarter. The number of points scored by the Eagles in each of the four quarters formed a quadratic sequence $(a, a+k, a+4k, a+9k)$, and the number of points scored by the Panthers in each of the four quarters formed an arithmetic sequence $(b, b+d, b+2d, b+3d)$. At the end of the final quarter, the Eagles had won by two points. Neither team scored more than 100 points. Determine the total number of points scored by both teams in the first half.

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