
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 sequence $\{a_n\}$, where $a_3$ and $a_{10}$ are the two roots of the equation $x^2 - 3x - 5 = 0$. If $\{a_n\}$ is an arithmetic sequence, then find the value of $a_5 + a_8$; if $\{a_n\}$ is a geometric sequence, then find the value of $a_6 \cdot a_7$.

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