
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 password lock with a password consisting of three digits. The lock can only be opened when we correctly input the number at each position. Currently, we do not know the password. When entering $246$, it prompts that 1 digit is correct and in the right position; when entering $258$, it prompts that 1 digit is correct but in the wrong position; when entering $692$, it prompts that 2 digits are correct but all in the wrong positions; when entering $174$, it prompts that none of the digits are correct; when entering $419$, it prompts that 1 digit is correct but in the wrong position. What is the correct password?

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