
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
Find all the real numbers  $k$  that have the following property: For any non-zero real numbers  $a$  and  $b$ ,  it is true that at least one of the following numbers:   $$ a, b,\frac{5}{a^2}+\frac{6}{b^3} $$  is less than or equal to  $k$ .

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