
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 $a$ and $h$ be positive numbers. Given that $(a+\frac{h}{2a})^{2}=a^{2}+h+(\frac{h}{2a})^{2}$, when $\frac{h}{2a}$ is very small (here it is agreed that $\frac{h}{2a}＜0.1$), $(\frac{h}{2a})^{2}≈0$. Therefore, $(a+\frac{h}{2a})^{2}≈a^{2}+h$, so $\sqrt{a^{2}+h}≈a+\frac{h}{2a}(*).$ By using $\left(*\right)$, we can approximate the square root of certain numbers, such as $\sqrt{10005}=\sqrt{100^{2}+5}≈100+\frac{5}{2×100}=100.025$. Calculate the approximate value of $\sqrt{14406}$ as ____.

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