
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
Let $a$, $b$, $c$, $x$, $y$, $z$ be positive numbers, and $a^{2}+b^{2}+c^{2}=10$, $x^{2}+y^{2}+z^{2}=40$, $ax+by+cz=20$. Express $\dfrac {a+b+c}{x+y+z}$ in a simplified fraction.

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