
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
Given that \(a, b, c, d\) are all prime numbers and \(a > 3\), \(b > 6\), \(c > 12\), and \(d\) are such that \(a^2 - b^2 + c^2 - d^2 = 1749\). Find all possible values of \(a^2 + b^2 + c^2 + d^2\).

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