
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 the real numbers \(a, b, c, x, y, z\):

$$
\begin{aligned}
& a^{2}+b^{2}+c^{2}=25 \\
& x^{2}+y^{2}+z^{2}=36 \\
& a x+b y+c z=30
\end{aligned}
$$

What is the value of the quotient \(\frac{a+b+c}{x+y+z}\)?

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