
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 $p,$ $q,$ $r,$ $u,$ $v,$ and $w$ are positive and $p^2 + q^2 + r^2 = 49,$ $u^2 + v^2 + w^2 = 64,$ and $pu + qv + rw = 56,$ compute
\[\frac{p + q + r}{u + v + w}.\]

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