
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
Kevin is trying to solve an economics question which has six steps. At each step, he has a probability  $p$  of making a sign error. Let  $q$  be the probability that Kevin makes an even number of sign errors (thus answering the question correctly!). For how many values of  $0 \le p \le 1$  is it true that  $p+q=1$ ?

*Proposed by Evan Chen*

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