
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
Before the start of the school year, the school's general affairs department was arranging dormitories for new students and did some precise calculations. If each dormitory houses 4 students, then there would be 20 students without accommodation. If each dormitory houses 8 students, then one of the dormitories would be neither full nor empty, with the rest being completely full. The question is, how many new students need accommodation in total? And how many dormitories are provided for them?

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