
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
Let \( p, q, r, \) and \( s \) be the roots of the polynomial \[ x^4 + 6x^3 + 13x^2 + 7x + 3 = 0. \] Find the value of \[ \frac{1}{pqr} + \frac{1}{pqs} + \frac{1}{prs} + \frac{1}{qrs}. \]

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