
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 real numbers $x$, $y$, and defining a new operation $x \ast y = ax + by + 1$, where $a$, $b$ are constants, and the right side of the equation is addition and multiplication as usual. If $3 \ast 5 = 15$ and $4 \ast 7 = 28$, then $1 \ast 1 = \_\_\_\_$.

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