
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, there are 2 one-cent coins, 4 five-cent coins, and 6 ten-cent coins. Six coins are drawn in sequence without replacement, and each coin has an equal probability of being selected. Calculate the probability that the total value of the drawn coins is at least 50 cents.

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