
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
Given the sequence \(\{a_n\}: a_n = 1 - \frac{2^{2^n}}{2^{2^{n+1}} + 1}\), denote \(T_n = a_0 a_1 \cdots a_n\). Then \(\lim_{n \rightarrow +\infty} T_n =\) ________.

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