
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
Determine the value of the expression  $x^2 + y^2 + z^2$ , 

if  $x + y + z = 13$  ,  $xyz= 72$  and  $\frac1x + \frac1y + \frac1z = \frac34$ .

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