
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
How many ordered pairs \((a,b)\) such that \(a\) is a positive real number and \(b\) is an integer between \(3\) and \(203\), inclusive, satisfy the equation \((\log_b a)^{2021}=\log_b(a^{2021})?\)
**A)** 200  
**B)** 201  
**C)** 602  
**D)** 603  
**E)** 606

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