
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 sequence ${a_n}$ satisfying $a_1=1$, $a_2=2$, $a_3=3$, $a_{n+3}=a_n$ ($n\in\mathbb{N}^*$). If $a_n=A\sin(\omega n+\varphi)+c$ $(ω>0,|\varphi|<\frac{\pi}{2})$, find the real number $A$.

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