
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 \(a_{1}, a_{2}, \ldots, a_{n}\) be a sequence of distinct positive integers such that \(a_{1} + a_{2} + \cdots + a_{n} = 2021\) and \(a_{1} a_{2} \cdots a_{n}\) is maximized. If \(M = a_{1} a_{2} \cdots a_{n}\), compute the largest positive integer \(k\) such that \(2^{k} \mid M\).

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