
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 graphs of the functions \( y = x^2 + ax + b \) and \( y = x^2 + cx + d \) intersect at the point with coordinates \( (1,1) \). Compare \( a^5 + d^6 \) and \( c^6 - b^5 \).

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