
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
A bondholder's bonds have different serial numbers. In the first draw, five bond serial numbers were drawn: two numbers were drawn 3 times each, one number was drawn 2 times, and two numbers were drawn 1 time each. What is the probability that the bondholder did not win despite having 10 chances? (It is known that each series consists of $1000$ bonds, and out of each series, only one group of 100 bonds wins.)

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