
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 $a,$ $b,$ $c,$ $x,$ $y,$ and $z$ be positive real numbers such that $a^2 + b^2 + c^2 = 49,$ $x^2 + y^2 + z^2 = 64,$ and $ax + by + cz = 56.$ Compute
\[\frac{a + b + c}{x + y + z}.\]

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