
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 function: $y=a_{n}x^{2}(a_{n}\neq 0,n\in\mathbb{N}^{*})$ whose graph has a tangent line slope of $2a_{n-1}+1(n\geqslant 2,n\in\mathbb{N}^{*})$ at $x=1$, and when $n=1$, its graph passes through the point $(2,8)$, find the value of $a_{7}$.

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