
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 the newly built school dormitory, there are some double rooms, and the rest are triple rooms. Overall, the dormitory can accommodate more than 30 but less than 70 places. When $\frac{1}{5}$ of the available places were filled, the number of unfilled places turned out to be the total number of places if the number of double rooms were equal to the actual number of triple rooms, and the number of triple rooms were equal to the actual number of double rooms. How many places can the dormitory accommodate?

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