
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 all natural numbers \( N < 10000 \) such that \( N = 26 \cdot S(N) \), where \( S(N) \) denotes the sum of the digits of the number \( N \).

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