
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 the sets \( A = \{2, 4, a^3 - 2a^2 - a + 7\} \) and \( B = \{-4, a + 3, a^2 - 2a + 2, a^3 + a^2 + 3a + 7\} \), and \( A \cap B = \{2, 5\} \), find the possible values of \( a \) that form a set.

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