
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 natural numbers $a$, $b$, and $c$, define a new operation $\ast$, such that $(a \ast b) \ast c = a \ast (bc)$ and $(a \ast b)(a \ast c) = a \ast (b+c)$. Determine the value of $2 \ast 4$.

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