
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
There are no more than 200 installations of 3 types altogether. Installations of type 2 are 4 times more numerous than type 1, and the number of type 3 installations is a multiple of the number of type 1 installations. If the number of type 3 installations were 5 times more, they would be 99 more than the number of type 2 installations. Find the number of installations of each type.


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