
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
Determine the range of \( x \) defined by:
\[ x = \frac{a_1}{2} + \frac{a_2}{3^2} + \frac{a_3}{3^3} + \cdots + \frac{a_{25}}{3^{25}} \]
where \( a_1 \) is $1$ or $2$, \( a_2, a_3, \ldots, a_{25} \) are either $0$ or $1$.
A) \( 0 \leq x < 1/2 \)
B) \( 1/2 \leq x < 7/6 \)
C) \( 2/3 \leq x < 5/4 \)
D) \( 3/4 \leq x < 4/3 \)

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