
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
If the integer \( k \) is added to each of the numbers \( 49 \), \( 324 \), and \( 625 \), one obtains the squares of three terms of an arithmetic series such that the common difference of the original series is \( d \). Find \( k \) and \( d \).

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