
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
Determine how many ordered pairs \((a, b)\) such that \(a\) is a positive real number other than 1 and \(b\) is an integer between 1 and 300, inclusive, satisfy both the equations \((\log_b a)^5 = \log_b (a^5)\) and \(\frac{a^{10}}{b^{2}} = 1\).
A) 0
B) 200
C) 298
D) 300

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