
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
Patchouli is taking an exam with  $k > 1$  parts, numbered Part  $1, 2, \dots, k$ . It is known that for  $i = 1, 2, \dots, k$ , Part  $i$  contains  $i$  multiple choice questions, each of which has  $(i+1)$  answer choices. It is known that if she guesses randomly on every single question, the probability that she gets exactly one question correct is equal to  $2018$  times the probability that she gets no questions correct. Compute the number of questions that are on the exam.

*Proposed by Yannick Yao*

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