
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
Find the number of 7-digit integers formed by some or all of the five digits, namely, 0, 1, 2, 3, and 4, such that these integers contain none of the three blocks 22, 33, and 44.

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