
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
During a basketball game, the scores of the first team in each of the four quarters formed an arithmetic sequence, while the scores of the second team formed a geometric sequence. The game ended with the first team winning by 2 points, and the total score of neither team exceeded 100 points. What was the total number of points scored by both teams in the first half?
A) 29
B) 30
C) 31
D) 32
E) 33

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