
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 $a,$ $b,$ $c,$ $u,$ $v,$ $w$ are positive and $a^2 + b^2 + c^2 = 9,$ $u^2 + v^2 + w^2 = 49,$ and $au + bv + cw = 21,$ compute \[\frac{a + b + c}{u + v + w}.\]

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