
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 geometric sequence $\{a_n\}$ consists of positive terms, and it is given that $a_1 + 2a_2 = 1$ and $a_3^2 = 4a_2a_6$.
1. Find the general formula for the sequence $\{a_n\}$.
2. Let $b_n + 2 = 3\log_2 \frac{1}{a_n}$. Find the sum of the first $n$ terms of the sequence $\{a_nb_n\}$.

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