
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
Which positive numbers \(x\) satisfy the equation \(\left(\log_2 x\right)\left(\log_x 7\right) + \log_{10} 7 = \log_2 7\)?
A) only \(2\) and \(7\)
B) \(2\), \(7\), and \(14\)
C) only numbers of the form \(7^n \cdot 2^m\), where \(n\) and \(m\) are nonnegative integers
D) all positive \(x\) not equal to 1
E) none of these

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