
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 that \(a_{1}, a_{2}, \cdots, a_{25}\) are either 0 or 2, determine the possible range of values of \(x\), where \(x=\frac{a_{1}}{3}+\frac{a_{2}}{3^{2}}+\cdots+\frac{a_{25}}{3^{25}}\).

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