
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
Using mathematical induction, demonstrate that for $n>1$, the following inequality holds: $$1 + \frac{1}{2} + \frac{1}{3} + \ldots + \frac{1}{2^n - 1} < n.$$ During the second step of the proof when establishing the transition from $n=k$ to $n=k+1$, determine the number of additional terms added to the left side.

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