
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
Point \\(P\\) is on a conic section, with \\({{F}\_{1}}\\) and \\({{F}\_{2}}\\) being the left and right foci, respectively. If \\(\left| P{{F}\_{1}} \right|:\left| {{F}\_{1}}{{F}\_{2}} \right|:\left| P{{F}\_{2}} \right|=4:3:2\\), then the eccentricity \\(e= \\)\_\_ or \_\_\_\_.

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