
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 two sequences $\{a_n\}$ and $\{b_n\}$ satisfying $a_1=2, b_1=1$ and $\begin{cases}a_n= \dfrac{3}{4}a_{n-1}+ \dfrac{1}{4}b_{n-1}+1 \\ b_n= \dfrac{1}{4}a_{n-1}+ \dfrac{3}{4}b_{n-1}+1\end{cases} \left(n\geqslant 2,n\in\mathbb{N}^*\right)$, then the value of $(a_3+b_3)\cdot(a_4-b_4)$ is.

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