
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
You have a set of n biased coins. The mth coin has a probability of \( \frac{1}{2m+1} \) of landing heads (for \( m = 1, 2, ... , n \)) and the results for each coin are independent. What is the probability that if each coin is tossed once, you get an odd number of heads?

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