
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
Given that the game was tied after the first quarter, the points scored by Team Alpha and Team Beta in the first quarter are equal, and both teams' total points form increasing geometric and arithmetic sequences, respectively. Additionally, the game concluded with Team Alpha winning by 3 points, and no team scored more than 120 points total. 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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