
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 given quadratic trinomial \( f(x) = x^2 + px + q \) has two roots, one of which coincides with the value of this trinomial at point 0, and the other coincides with the value at point 1. Find the value of this trinomial at point 6.

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