
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 that \\(F_{1}\\) and \\(F_{2}\\) are the left and right foci of the hyperbola \\(3x^{2}-y^{2}=3a^{2}(a > 0)\\), respectively, and \\(P\\) is an intersection point of the parabola \\(y^{2}=8ax\\) with the hyperbola. If \\(|PF_{1}|+|PF_{2}|=12\\), then the equation of the directrix of the parabola is \_\_\_\_\_\_.

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