
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
When Vitya was a first grader, he had a set of 12 number cards: two cards with the number 1, two cards with the number 2, and so on up to the number 6. Vitya placed them on the table in a random order from left to right, and then removed the first 1, the first 2, the first 3, and so on. For example, if Vitya initially had the sequence 434653625112, the resulting sequence would be 436512. What is the probability that the sequence left on the table is 123456?

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