
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 $x$ and $y$ be real numbers such that
\[9x^2 + 15xy + 8y^2 = 1.\]
Let $m$ and $M$ be the minimum and maximum values of $3x^2 + 4xy + 3y^2$, respectively. Find the product $mM$.

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