
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
For a positive real number  $  [x] $  be its integer part. For example,   $[2.711] = 2, [7] = 7, [6.9] = 6$ .  $z$  is the maximum real number such that [ $\frac{5}{z}$ ] + [ $\frac{6}{z}$ ] = 7. Find the value of $ 20z$ .

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