
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
A sequence of real numbers \( a_{1}, a_{2}, \cdots a_{n}, \cdots \) is defined by the equation:
\[ a_{n+1} = 2^{n} - 3 a_{n}, \quad n = 0, 1, 2, \cdots . \]

1. Find the expression for \( a_{n} \) that depends on \( a_{0} \) and \( n \);
2. Determine \( a_{0} \) such that for any positive integer \( n \), \( a_{n+1} > a_{n} \).

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