
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>k</sub> = 1/(k+2) + 1/(k+3) + 1/(k+4) + ... + 1/(2k-1), where k ≥ 3, k ∈ N*. Find the value of S<sub>k+1</sub>.

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