
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
If \( a, b, c, x, y, \) and \( z \) are all real numbers, and
\[ a^2 + b^2 + c^2 = 25, \quad x^2 + y^2 + z^2 = 36, \quad a x + b y + c z = 30, \]
find the value of the expression \(\frac{a+b+c}{x+y+z}\).

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