
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
Using the 26 letters of the English alphabet to form permutations without repetition, determine the number of permutations that exclude the substrings "dog", "god", "gum", "depth", and "thing".

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