
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 ${(1+2x)}^{n}={a}_{0}+{a}_{1}x+⋅⋅⋅+{a}_{n}{x}^{n}$, where $a_{0}+a_{1}+\cdot \cdot \cdot +a_{n}=729$, find the value of ${a}_{0}-{a}_{1}+{a}_{2}-{a}_{3}+⋅⋅⋅+{(-1)}^{n}⋅{a}_{n}$.

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