
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
There are $n$ numbers, the first one is denoted as $a_1$, the second as $a_2$, ..., the $n$-th as $a_n$. If $a_1 = \frac{1}{2}$, and starting from the second number, each number equals the reciprocal of "1 minus the number before it".

(1) Find the values of $a_2$, $a_3$, $a_4$;  
(2) Based on the results of (1), conjecture and write down the values of $a_{2010}$, $a_{2011}$, $a_{2012}$.

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