
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
What is the smallest positive integer \( n \) which cannot be written in any of the following forms?
- \( n = 1 + 2 + \cdots + k \) for a positive integer \( k \).
- \( n = p^k \) for a prime number \( p \) and integer \( k \).
- \( n = p + 1 \) for a prime number \( p \).
- \( n = pq \) for some distinct prime numbers \( p \) and \( q \).

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