
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

23. Two friends, Marco and Ian, are talking about their ages. Ian says, "My age is a zero of a polynomial with integer coefficients."
Having seen the polynomial \( p(x) \) Ian was talking about, Marco exclaims, "You mean, you are seven years old? Oops, sorry I miscalculated! \( p(7) = 77 \) and not zero."
"Yes, I am older than that," Ian's agreeing reply.
Then Marco mentioned a certain number, but realizes after a while that he was wrong again because the value of the polynomial at that number is 85.
Ian sighs, "I am even older than that number."
Determine Ian's age.

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