
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 high school basketball game between the Eagles and the Lions, the Eagles started leading by 2 points at the end of the first quarter. The number of points scored by the Eagles in each of the four quarters formed an increasing arithmetic sequence, while the number of points scored by the Lions in each of the four quarters formed an increasing geometric sequence. At the end of the third quarter, the aggregate score was tied. Neither team scored more than 100 points in total. Find the total number of points scored by the two teams at the end of the game.

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