
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
Given \( h(x) \) is a polynomial with leading coefficient 1, whose roots are \( 1/(p^2+1), 1/(q^2+1), 1/(r^2+1) \), where \( p, q, \) and \( r \) are the roots of \( f(x) = x^3 + ax^2 + bx + c \), with \( a, b, \) and \( c \) being positive integers such that \( a < b < c \), express \( h(1) \) in terms of \( a, b, \) and \( c \).

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