
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
An arithmetic sequence with real number terms has a common difference of 4, and the square of its first term plus the sum of the remaining terms does not exceed 100. The maximum number of terms this sequence can have is \_\_\_\_\_\_\_.

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