
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

Let \( p, q \geq 0 \) with \( p + q = 1 \) and \( m, n \in \mathbb{N}^{*} \). Show the inequality:

$$
\left(1 - p^m\right)^n + \left(1 - q^n\right)^m \geq 1
$$

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