
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 square flag features a symmetric green cross with an orange square at the center on a white background. The cross (including both the green arms and the orange center) covers 40% of the flag's total area. If the green area is 32% of the flag's area, what is the width of the green arms, assuming the flag has a side length of 1 unit?

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