
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
In the equation
\[ A^{A A} + A A = B, B B C, D E D, B E E, B B B, B B E \]
the letters \( A, B, C, D \) and \( E \) represent different base 10 digits (so the right-hand side is a sixteen-digit number and \( A A \) is a two-digit number). Given that \( C = 9 \), find \( A, B, D \) and \( E \).

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