
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 $y = a_nx^2$ ($a_n \neq 0$, $n \in \mathbb{N}^*$), the slope of the tangent line at $x = 1$ is $2a_{n-1} + 1$ ($n \geq 2$), 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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