
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 the hyperbola $$\frac {x^{2}}{a^{2}} - \frac {y^{2}}{b^{2}} = 1$$ ($a > 0$, $b > 0$) has an eccentricity of $$\frac {2 \sqrt {3}}{3}$$, and the focal distance is $2c$, with $2a^2 = 3c$. A point $P$ on the hyperbola satisfies $$\overrightarrow {PF_{1}} \cdot \overrightarrow {PF_{2}} = 2$$ ($F_{1}$ and $F_{2}$ are the left and right foci, respectively), then $| \overrightarrow {PF_{1}} | \cdot | \overrightarrow {PF_{2}} | = \boxed{4}$.

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