
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
$\varphi\left(p^{\lambda} q^{\mu}\right)=\left(p^{\lambda}-p^{\lambda-1}\right)\left(q^{\mu}-q^{\mu-1}\right)$ and in general:

$\varphi\left(p_{1}^{\lambda_{1}} p_{2}^{\lambda_{2}} \cdots p_{n}^{\lambda_{n}}\right)=\left(p_{1}^{\lambda_{1}}-p_{1}^{\lambda_{1}-1}\right) \left(p_{2}^{\lambda_{2}}-p_{2}^{\lambda_{2}-1}\right) \ldots\left(p_{n}^{\lambda_{n}}-p_{n}^{\lambda_{n}-1}\right).$

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