
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
What is the coefficient of \(x^5\) when 
$$x^6 - 2x^5 + 3x^4 - 4x^3 + 5x^2 - 6x + 7$$ 
is multiplied by 
$$3x^4 - 4x^3 + 5x^2 + 6x - 8$$ 
and the like terms are combined?

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