
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
In a room there are  $144$  people. They are joined by  $n$  other people who are each carrying  $k$  coins. When these coins are shared among all  $n + 144$  people, each person has  $2$  of these coins. Find the minimum possible value of  $2n + k$ .

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