
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 the game "What? Where? When?" 13 envelopes with questions from the TV audience are contested. The envelopes are chosen randomly one by one using a spinner. If the experts answer correctly, they earn a point; if incorrect, the TV audience earns a point. The game ends as soon as one of the teams reaches 6 points.

Assume that the teams of Experts and TV Audiences are evenly matched.
a) Find the expected number of points earned by the team of Experts over 100 games.

b) Find the probability that envelope number 5 will be chosen in the next game.

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