
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

Find the smallest even natural number \( a \) such that \( a + 1 \) is divisible by \( 3 \), \( a + 2 \) is divisible by \( 5 \), \( a + 3 \) is divisible by \( 7 \), \( a + 4 \) is divisible by \( 11 \), and \( a + 5 \) is divisible by \( 13 \).

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