
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
The sequence  $(x_n)_{n\geqslant 0}$  is defined as such:  $x_0=1, x_1=2$  and  $x_{n+1}=4x_n-x_{n-1}$ , for all  $n\geqslant 1$ . Determine all the terms of the sequence which are perfect squares.

*George Stoica, Canada*

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