
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
Can the position of a chess piece on the board be determined by the following equation, where \( x \) and \( y \) denote the row and column numbers of the square, respectively:

\[ 
x^2 + xy - 2y^2 = 13 
\]

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