
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
You are given an algorithm to estimate the area of the region $\Omega$ enclosed by the curves $y=x^{2}$ and $y=4$ using a computer random simulation method. The algorithm is as follows:

Step 1: Generate two uniform random numbers $a$, $b$ in the interval $[0,1]$ using a computer.
Step 2: Transform the random numbers $a$, $b$ as follows: $\begin{cases} a_{1}=4\cdot a-2\\b_{1}=4b\end{cases}$ to obtain the point $A(a_{1},b_{1})$.
Step 3: Determine whether the coordinates of point $A(a_{1},b_{1})$ satisfy $b_{1} < a_{ 1 }^{ 2 }$.
Step 4: Accumulate the number $m$ of generated points $A$ and the number $n$ of points $A$ satisfying $b_{1} < a_{ 1 }^{ 2 }$.
Step 5: If $m$ is less than $M$ (a preset number), return to Step 1; otherwise, output $n$ and terminate the algorithm.

If $M=100$ and the output $n=34$, then the area of the region $\Omega$ can be estimated using the random simulation method as $\_\_\_\_\_\_$ (keep two decimal places).

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