
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
Let S<sub>n</sub> be the sum of the first n terms of the sequence {a<sub>n</sub>}, satisfying a<sub>n</sub><sup>2</sup>+1=2a<sub>n</sub>S<sub>n</sub>, and a<sub>n</sub> > 0, then a<sub>100</sub>\=\_\_\_\_\_\_．

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