
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
We wrote a three-digit natural number composed of mutually distinct non-zero digits on a clean board using yellow chalk. Then, we wrote all other three-digit numbers that can be obtained by rearranging the digits of the yellow number in white chalk. The arithmetic mean of all the numbers on the board was 370. We underlined each number smaller than the yellow one. The underlined numbers were exactly three, and their arithmetic mean was 205. Determine the yellow number.

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