
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 the line $x=2a$ intersects with one asymptote of the hyperbola C: $$\frac {x^{2}}{a^{2}}- \frac {y^{2}}{b^{2}}=1(a＞0，b＞0)$$ at point P, and the left and right foci of the hyperbola C are $F_1$ and $F_2$ respectively, with $$cos∠PF_{2}F_{1}=- \frac {1}{4}$$, find the eccentricity of the hyperbola C.

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