
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 five-member committee consisting of $A, B, C, D,$ and $E$ makes decisions by voting, and resolutions are accepted by a majority vote. The smartest member $A$ makes incorrect decisions in only 5\% of the cases. (For simplicity, assume that every resolution is either correct or incorrect.) $B, C,$ and $D$ make errors in 10\% of the cases, while $E$ makes mistakes in 20\% of them.

a) In what percentage of cases does the committee make an incorrect decision?

b) $E$, the “least intelligent” member of the committee, has decided to always vote in the same way as $A$ from now on. How does this decision change the rate of incorrect decisions?

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