
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
A biased coin with a probability $\frac{4}{5}$ of landing heads and a second fair coin are tossed alternatingly, starting with the biased coin, for a total of 40 tosses. What is the probability that the total number of heads is even?
A) $\frac{1}{2}$
B) $\frac{1}{2}(1 - (\frac{2}{5})^{40})$
C) $\frac{1}{2}(1 + (\frac{2}{5})^{40})$
D) $(\frac{2}{5})^{40}$

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