
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
The game circle in the TV quiz show "What? Where? When?" is divided into 13 equal sectors, numbered from 1 to 13. At the beginning of the game, each sector contains an envelope with a question. Players choose a random sector using a spinning arrow. If this sector has already been selected before, the envelope in it is already gone, and then the next clockwise sector plays. If it is also empty, the next one plays, and so on until an occupied sector is found. Before the break, players have played six sectors.

a) Which is more likely: that the chosen sectors include sector number 1 or that the chosen sectors include sector number 8?

b) Find the probability that the six sectors played were consecutively numbered from 1 to 6.

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