
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
Two bullets are placed in two consecutive chambers of a 6-chamber pistol. The cylinder is then spun. The pistol is fired but the first shot is a blank. Let \( p \) denote the probability that the second shot is also a blank if the cylinder is spun after the first shot and let \( q \) denote the probability that the second shot is also a blank if the cylinder is not spun after the first shot. Find the smallest integer \( N \) such that
\[ 
N \geq \frac{100 p}{q} .
\]

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