
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 diagram, the rectangle has a width \( w \), a length of \( 10 \), and a perimeter of \( 30 \). What is the ratio of its width to its length? Assume the diagram is similar to the original with appropriate adjustments to the labels for width and length.

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