
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
Using the Monte Carlo method to calculate the area enclosed by $y=x^2+1$ and $y=5$, first generate two groups of uniform random numbers between 0 and 1, denoted $a_1=\text{RAND}$ and $b_1=\text{RAND}$, then perform translation and scaling transformations as $a=4a_1-2$ and $b=4b_1+1$. After 1000 experiments, the number of sample points that fall within the desired area for the first 998 trials is 624. Given the uniform random numbers (0.3, 0.1) and (0.9, 0.7) generated by the last two experiments, calculate the estimated area obtained from this simulation.

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