
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
Compute the largest possible number of distinct real solutions for  $x$  to the equation \[x^6+ax^5+60x^4-159x^3+240x^2+bx+c=0,\] where  $a$ ,  $b$ , and  $c$  are real numbers.

[i]Proposed by Tristan Shin

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