
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 a positive integer \( n \) and a set of \( k \) weights (each with positive integer grams) along with a balance scale, it is possible to measure the weight of any object weighing \( 1, 2, \dots, n \) grams. Find the minimum value of \( k \), denoted as \( f(n) \).

(Nationwide High School Mathematics Competition Supplemental Problem, 1999)

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