
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
For rational numbers $x, y$, define a new operation "$\ast$" such that $x \ast y = mx + ny + p$, where $m, n, p$ are constants, and the operations on the right side of the equation are the usual addition and multiplication. Given that $3 \ast 5 = 30$ and $4 \ast 6 = 425$, find the value of $8 \ast 10$.

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