
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 $64cm$ long iron wire is cut into two unequal parts, each folded into a square.<br/>$(1)$ If the area of the large square is $2.25$ times the area of the small square, then the side length of the small square is ______ $cm$;<br/>$(2)$ If the sum of the areas of the two squares is $160cm^{2}$, how should the wire be cut?

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