
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
An urn contains balls of \( k \) different colors; there are \( n_{i} \) balls of the \( i \)-th color. Balls are drawn at random from the urn, one by one, without replacement. Find the smallest number of draws necessary for getting \( m \) balls of the same color.

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