
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 collegiate basketball game, the Tigers and Lions were tied at the end of the first quarter, and the point difference at the end of the fourth quarter is 4 points. The Tigers scored points in each of the four quarters that formed an increasing geometric sequence, while the Lions scored points in each of the four quarters that formed an increasing arithmetic sequence. Neither team scored more than 120 points in total. Find the total number of points scored by the two teams in the first half.

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