
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
A large cube with an edge length of an integer $a$ can be divided into 280 small cubes, among which 279 are cubes with an edge length of 1, and the remaining one cube also has an integer edge length. What is the value of $a$?

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