
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 the left and right vertices of the hyperbola $x^2 - y^2 = 6$ be $A_1$ and $A_2$, respectively. Let $P$ be a point on the right branch of the hyperbola, located in the first quadrant. The slopes of lines $PA_1$ and $PA_2$ are $k_1$ and $k_2$, respectively. Find the value of $k_1 \cdot k_2$.

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