
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
Let the derivative of the function $f(x)$ be denoted as $f^{(1)}(x)$, the derivative of $f^{(1)}(x)$ as $f^{(2)}(x)$, ..., and the derivative of $f^{(n-1)}(x)$ as $f^{(n)}(x)$ (where $n \in \mathbb{N}^*$). If $f(x)$ can be differentiated $n$ times, then $f(x)$ can be approximately represented as: $f(x) \approx f(0) + \frac{f^{(1)}(0)}{1!}x + \frac{f^{(2)}(0)}{2!}x^2 + \frac{f^{(3)}(0)}{3!}x^3 + \ldots + \frac{f^{(n)}(0)}{n!}x^n$. If we take $n=4$, according to this conclusion, we can approximately estimate $\cos(2) \approx$ \_\_\_\_\_\_ (expressed as a fraction).

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