
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 from \( 20 \) to \( 220 \), inclusive, satisfy the equation \( (\log_b \sqrt{a})^{2017} = \log_b(a^{2017}) \)?
**A)** 600
**B)** 602
**C)** 603
**D)** 604
**E)** 606

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