
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 Team Alpha and Team Beta, the game was tied at the end of the first quarter. The number of points scored by Team Alpha in the four quarters formed an increasing geometric sequence while Team Beta’s scores formed an increasing arithmetic sequence. At the end of the game, Team Alpha won by two points, and the total score for both teams combined was under 200 points. What was the total number of points scored by both teams in the first half?
A) 27
B) 29
C) 30
D) 32
E) 34

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