
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 city's Spring Festival gala originally planned 10 programs, but the director decided to add 3 programs related to "Disaster Relief from Ice" at the end. The relative order of the already arranged 10 programs remains unchanged, and the 3 new programs cannot be adjacent to each other. The total number of arrangements for the gala program list is $\boxed{\text{number}}$.

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