
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
Given the equation $\sin 1^{\circ}+\sin 2^{\circ}+\sin 3^{\circ}+\sin 4^{\circ}+\ldots+\sin x^{\circ}=\sin 1^{\circ}\cdot\sin 2^{\circ}\cdot\sin 3^{\circ}\cdot\sin 4^{\circ}\cdot\ldots\cdot\sin x^{\circ}$, where $x$ is a positive integer, when $1\leqslant x\leqslant 90$, the number of $x$ that satisfies the equation is \_\_\_\_\_\_; when $1\leqslant x\leqslant 2017$, the number of $x$ that satisfies the equation is \_\_\_\_\_\_.

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