
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 a medium-sized class, there was a math written test with 2 problems, and each student solved at least one of them.

- The number of students who solved only one problem was one less than twice the number of students who solved both problems.
- Students who solved both problems were given 1 new problem as homework for the next class.
- Students who only solved the more difficult problem were given 4 new problems as homework.
- Students who only solved the easier problem were given 1 new difficult problem as homework.
  
The total number of homework solutions submitted by the first two groups (both problems solvers and more difficult problem solvers) was equal to the number of homework solutions submitted by the third group (easier problem solvers).

How many students are in the class?

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