
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
For a set of real numbers \( A \), let \( A - A \) be the set of distinct pairwise differences of \( A \); that is,
\[ A - A := \{ a - b : a, b \in A \} \]

If \( |A - A| = 25 \), find the sum of all possible values of \( |A| \).

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