
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
Reading material: If we can find two positive integers $x$ and $y$ such that $x+y=a$ and $xy=b$, then $\sqrt{a+2\sqrt{b}}=\sqrt{{(\sqrt{x})}^{2}+{(\sqrt{y})}^{2}+2\sqrt{x}\cdot\sqrt{y}}=\sqrt{{(\sqrt{x}+\sqrt{y})}^{2}}=\sqrt{x}+\sqrt{y}$. In this case, we call $\sqrt{a+2\sqrt{b}}$ as "harmonic quadratic radical", and the above process is called simplifying "harmonic quadratic radical". For example: $\sqrt{3+2\sqrt{2}}=\sqrt{{1}^{2}+{(\sqrt{2})}^{2}+2\times1\times\sqrt{2}}=\sqrt{{(1+\sqrt{2})}^{2}}=1+\sqrt{2}$. According to the reading material, solve the following problem: Simplify the "harmonic quadratic radical" $\sqrt{11+2\sqrt{28}}=\_\_\_\_\_\_$.

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