
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
In a box containing $3$ pennies ($1$ cent each), $5$ nickels ($5$ cents each), and $4$ dimes ($10$ cents each), you draw six coins without replacement. Each coin has an equal probability of being selected. What is the probability that the value of the coins drawn totals at least $40$ cents?
A) $\frac{12}{77}$
B) $\frac{10}{77}$
C) $\frac{15}{77}$
D) $\frac{15}{924}$

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