
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
One coin of value at least $1$ cent is drawn from a box containing $3$ pennies, $5$ nickels, $4$ dimes, and $2$ quarters, and then another coin is drawn from the remaining coins, then another, and so on, up to a total of eight coins being drawn without replacement, with each coin drawing having an equal probability of being chosen, find the probability that the value of the coins drawn is at least $1$ cent.

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