
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 $(a,b)$, where $a$ is a positive real number and $b$ is an integer from $1$ to $100$ inclusive, satisfy the equation $(\log_b a)^{2023}=\log_b(a^{2023})?$
A) 100  
B) 200  
C) 300  
D) 400  
E) 500

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