
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
Construct an arbitrary segment $AS$, then construct a circle $k$ with center $S$ that passes through point $A$.

1. Construct points $E, F, G$ on circle $k$ such that together with point $A$, they form a rectangle $AEFG$. Find at least two solutions.
2. Construct points $B, C, D$ on circle $k$ such that together with point $A$, they form a square $ABCD$.

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