
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
There is a balance and one weight of $1$, $2$, $4$, and $10$. At each step, we select any weight and put it on the left or right side of the balance until all weights are placed on both sides of the balance. However, during the process of putting the weights, we find that the pointer of the balance will not tilt to the right of the scale. In this way, determine the number of ways to place the weights.

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