
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, a rectangle has a width \( w \), a length of \( 10 \), and a perimeter of \( 30 \). What is the ratio of its width to its length? Illustrate the rectangle and label the sides with the given measurements.

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