
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
Consider all finite sequences of positive real numbers each of whose terms is at most  $3$  and the sum of whose terms is more than  $100$ . For each such sequence, let  $S$  denote the sum of the subsequence whose sum is the closest to  $100$ , and define the *defect* of this sequence to be the value  $|S-100|$ . Find the maximum possible value of the defect.

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