
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
A room is 25 feet long, 15 feet wide, and 10 feet high. Find the ratio of the height of the room to the sum of its perimeter and height. Express your answer in the form $a:b$.

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