
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
Given that the product of the first $n$ terms of the positive sequence $\{a_n\}$ is $T_n$, and the point $(T_n, n^2 - 15n)$ is on the graph of the function $y = \log_{\frac{1}{2}}x$, calculate the sum of the first 10 terms of the sequence $\{\log_2 a_n\}$.

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