
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
The sequence $\{a_n\}$ satisfies the condition $a_n a_{n+1} a_{n+2} = a_n + a_{n+1} + a_{n+2}$ ($a_n a_{n+1} \neq 1$, $n \in \mathbb{N}^*$), with $a_1 = 1$ and $a_2 = 2$. If $a_n = A \sin(\omega n + \phi) + c$ ($\omega > 0$, $|\phi| < \frac{\pi}{2}$), find the value of the real number $A$.

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