
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
There are 9 sticks of different lengths ranging from 1 cm to 9 cm. Out of these sticks, what squares can be formed by their sides and in how many ways? The ways of forming a square are considered different if different sticks are used and not necessarily all sticks.

Is it possible to form squares with side lengths of 1 cm? 2 cm? ... 6 cm? Why? Is it possible to form a square with a side length of 7 cm? How would you do this? In how many different ways can it be done? Continue examining all possible cases. Is it possible to form a square with a side length of 12 cm or more? Why?

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