
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
In the binomial expansion of $(x- \sqrt {2})^{2006}$, the sum of the terms containing odd powers of $x$ is denoted as $S$. When $x= \sqrt {2}$, $S$ equals \_\_\_\_\_\_.

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