
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
We know that if a function $f(x)$ defined on a certain interval satisfies the inequality $\dfrac{f(x_{1})+f(x_{2})}{2} \leqslant f\left( \dfrac{x_{1}+x_{2}}{2}\right)$ for any two numbers $x_{1}, x_{2}$ in that interval, then the function $f(x)$ is called a convex function on that interval (briefly, convex). Similarly, for a sequence $\{a_{n}\}$, if for any positive integer $n$, the inequality $\dfrac{a_{n}+a_{n+2}}{2} \leqslant a_{n+1}$ always holds, then the sequence $\{a_{n}\}$ is called a convex sequence (briefly, convex sequence). Given a sequence $\{a_{n}\}$ that satisfies the following two conditions:
1. The sequence $\{a_{n}\}$ is a convex sequence, and $a_{1}=1$, $a_{10}=28$;
2. For positive integers $n(1 \leqslant n < 10, n \in \mathbb{N}^{*})$, it always holds that $|a_{n}-b_{n}| \leqslant 20$, where $b_{n}=n^{2}-6n+10$, then the range of the third term $a_{3}$ of the sequence $\{a_{n}\}$ is ______.

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