
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 $y_1, y_2, y_3, y_4, y_5$ be the roots of the polynomial $h(y) = y^5 - 3y^3 + 2,$ and let $p(y) = y^2 - 3.$ Find
\[p(y_1) p(y_2) p(y_3) p(y_4) p(y_5).\]

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