
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 two foci of the conic section \\(\Gamma\\) be \\(F_1\\) and \\(F_2\\), respectively. If there exists a point \\(P\\) on the curve \\(\Gamma\\) such that \\(|PF_1|:|F_1F_2|:|PF_2|=4:3:2\\), then the eccentricity of the curve \\(\Gamma\\) is \_\_\_\_\_\_\_\_

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