
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 math conference is expanding its lecture series and will now feature seven different lecturers. If Dr. Smith's lecture depends on Dr. Jones's lecture, and Dr. Lee's lecture depends on both Dr. Jones's and Dr. Smith's lecture, so that Dr. Smith must be scheduled at some time after Dr. Jones and Dr. Lee must be scheduled after both Dr. Jones and Dr. Smith, in how many orders can the seven lecturers be scheduled?

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