
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
An unfair coin has a $3/4$ probability of turning up heads. If this coin is tossed $40$ times, what is the probability that the total number of heads is odd?
A) $\frac{1}{2}$
B) $\frac{1}{2}(1 - \frac{1}{4^{40}})$
C) $\frac{3}{4}$
D) $\frac{1}{2}(1 + \frac{1}{4^{40}})$

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