
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 a geometric sequence $\{a_n\}$ where $a_n > 0$, and it satisfies $a_1 + a_3 = \frac{5}{16}$, $a_2 + a_4 = \frac{5}{8}$, find the minimum value of $\log_2(a_1a_2\ldots a_n)$.

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