
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 Team Falcon and Team Eagle, the game began with a tie in the first quarter. Team Falcon's scores over the four quarters followed a geometric sequence, while Team Eagle's scores followed an arithmetic sequence. At the end of the game, Team Falcon won by just two points. The total score of each team did not exceed 120 points in the game, and no team scored more than 36 points in a quarter. Calculate the combined score by both teams in the first half.

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