
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 all integers \( n \) and \( k \) such that \( n \geq k \geq 2 \), the probability that \( G \in \mathcal{G}(n, p) \) contains an independent set of \( k \) vertices is at most
$$
P[\alpha(G) \geqslant k] \leqslant \binom{n}{k} q^{\binom{k}{2}} .
$$

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