
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
G is a group generated by the two elements \( g \) and \( h \), which satisfy \( g^4 = 1 \), \( g^2 \neq 1 \), \( h^7 = 1 \), \( h \neq 1 \), and \( ghg^{-1}h = 1 \). The only subgroup containing \( g \) and \( h \) is G itself. Write down all elements of G which are squares.

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