
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
Compute the number of ways to tile a  $3\times5$  rectangle with one  $1\times1$  tile, one  $1\times2$  tile, one  $1\times3$  tile, one  $1\times4$ , and one  $1\times5$  tile. (The tiles can be rotated, and tilings that differ by rotation or reflection are considered distinct.)

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