
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 viewers are played. The envelopes are chosen one by one in random order using a spinner. If the experts answer correctly, they earn a point; if incorrectly, the viewers earn a point. The game ends as soon as one of the teams has scored 6 points. Assume that the strengths of the Experts and the Viewers teams are equal.

a) Find the mathematical expectation of the number of points scored by the Experts team over 100 games.

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

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