
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 ways to pave a $1 \times 10$ block with tiles of sizes $1 \times 1, 1 \times 2$ and $1 \times 4$, assuming tiles of the same size are indistinguishable. It is not necessary to use all the three kinds of tiles.

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