
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
The sequence \(b_1, b_2, \ldots\) is geometric with \(b_1 = b\) and a common ratio \(s\), where \(b\) and \(s\) are positive integers. Suppose that \(\log_4 b_1 + \log_4 b_2 + \cdots + \log_4 b_7 = 343\). Determine the number of possible ordered pairs \((b,s)\).

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