
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
Five cards have the numbers 101, 102, 103, 104, and 105 on their fronts. On the reverse, each card has one of five different positive integers: \(a, b, c, d,\) and \(e\) respectively. We know that \(a + 2 = b - 2 = 2c = \frac{d}{2} = e^2\).

Gina picks up the card which has the largest integer on its reverse. What number is on the front of Gina's card?

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