
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 $$f(x)= \begin{cases} \overset{log_{3}x,x>0}{4^{x},x\leq 0}\end{cases}$$, if the terminal side of angle α passes through point P(1, $$2 \sqrt {2}$$), find f(f(cosα)).

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