
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
There are $2n$ passengers on board an airliner, and the airline has loaded $n$ portions of chicken and $n$ portions of fish for them. It is known that a passenger prefers chicken with probability 0.5 and fish with probability 0.5. We will call a passenger dissatisfied if they are left with the option they do not prefer.

a) Find the most likely number of dissatisfied passengers.

b) Find the expected value of the number of dissatisfied passengers.

c) Find the variance of the number of dissatisfied passengers.

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