
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  $x,y,z>0$  such that  $$ (x+y+z)\left(\frac1x+\frac1y+\frac1z\right)=\frac{91}{10} $$  Compute  $$ \left[(x^3+y^3+z^3)\left(\frac1{x^3}+\frac1{y^3}+\frac1{z^3}\right)\right] $$  where  $[.]$  represents the integer part.

*Proposed by Marian Cucoanoeş and Marius Drăgan*

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