
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
Point \(Q\) has coordinates \((a+1, 4a+1)\) for some \(a > 1\), and lies on the line with equation \(y = ax + 3\). If \(O\) is the origin \((0, 0)\), determine the coordinates of the points \(P\) and \(R\) so that \(OPQR\) is a square with diagonal \(OQ\).

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