
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
It's pouring down rain, and the amount of rain hitting point  $(x,y)$  is given by   $$ f(x,y)=|x^3+2x^2y-5xy^2-6y^3|. $$  If you start at the origin  $(0,0)$ , find all the possibilities for  $m$  such that  $y=mx$  is a straight line along which you could walk without any rain falling on you.

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