
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 function $$f(x)= \frac {1}{3}x^{3}-ax+2a (a∈R)$$.
(1) When a=1, find the equation of the tangent line to the curve f(x) at the point (2, f(2));
(2) Draw a tangent line to y=f(x) passing through the point (2, 0). If the sum of the slopes of all tangent lines is 1, find the value of the real number a.

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