
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 television station used to broadcast 5 different commercial ads in sequence during a certain time slot. Now it has decided to add one more commercial ad and two different public service ads. It's required that the two public service ads neither play consecutively nor at the beginning or end of the sequence. Assuming the relative order of the original 5 commercial ads remains unchanged, how many different broadcast orders can there be?

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