
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
There is a number game that can produce a "black hole number" through the following steps: First, write down any natural number (hereinafter referred to as the original number); Second, write a new three-digit number, where the hundreds digit is the count of even digits in the original number, the tens digit is the count of odd digits in the original number, and the units digit is the total number of digits in the original number; For each subsequent step, apply the rule from the second step to the number obtained from the previous step, and continue this process until the number no longer changes. No matter what number you start with, after a few steps, the resulting natural number is always the same. This final number is called the "black hole number." Please try this with 2004 as an example (you may choose another natural number for verification, but it is not necessary to write out the verification process): 2004, after one step becomes ____, then changes to ____, then changes to ____, …, the "black hole number" is ____.

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