
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 \( S = \frac{2}{1 \times 3} + \frac{2^2}{3 \times 5} + \frac{2^3}{5 \times 7} + \cdots + \frac{2^{49}}{97 \times 99} \) and \( T = \frac{1}{3} + \frac{2}{5} + \frac{2^2}{7} + \cdots + \frac{2^{48}}{99} \), find \( S - T \).

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