
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
Given the four expressions: $2^{2} \lt 5 \lt 3^{2}$; $2.2^{2} \lt 5 \lt 2.3^{2}$; $2.23^{2} \lt 5 \lt 2.24^{2}$; $2.236^{2} \lt 5 \lt 2.237^{2}$. Using the method of rational number approximation of irrational numbers, estimate the approximate value of $\sqrt{5}$ accurate to $0.01$.

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