
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 $θ∈(0,π)$, and $sin⁡θ$, $cos⁡θ$ are the roots of the equation about $x$: $5x^{2}-x+m=0$, find the values of $sin⁡θ⋅cos⁡θ$ and $sin^{3}⁡θ+cos^{3}⁡θ$.

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