
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 that $T_n$ is the sum of the first $n$ terms of the sequence $\left\{ \frac{2^n + 1}{2^n} \right\}$, if $n > T_{10} + 1013$ always holds, then find the minimum value of the integer $n$.

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