
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
In the geometric sequence $\{a_n\}$, if $a_5 + a_6 + a_7 + a_8 = \frac{15}{8}$ and $a_6a_7 = -\frac{9}{8}$, then find the value of $\frac{1}{a_5} + \frac{1}{a_6} + \frac{1}{a_7} + \frac{1}{a_8}$.

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