
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
For any positive integer n, evaluate   $$ \sum_{i=0}^{\lfloor \frac{n+1}{2} \rfloor}
 {n-i+1 \choose i} $$  , where   $\lfloor n \rfloor$   is the greatest integer less than or equal to  $n$  .


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