
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
The polynomial  $x^3-kx^2+20x-15$  has  $3$  roots, one of which is known to be  $3$ . Compute the greatest possible sum of the other two roots.

*2015 CCA Math Bonanza Lightning Round #2.4*

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