
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 "$\ast$": $x \ast y = ax + by + c$, where $a, b, c$ are constants, and the right side of the equation involves the usual addition and multiplication operations. Given that $3 \ast 5 = 15$ and $4 \ast 7 = 28$, find the value of $1 \ast 1$.

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