
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 \( p \) and \( q \) represent two consecutive prime numbers. For some fixed integer \( n \), the set \( \{ n - 1, 3n - 19, 38 - 5n, 7n - 45 \} \) represents \( \{ p, 2p, q, 2q \} \), but not necessarily in that order. Find the value of \( n \).

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