
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 real sequence $a_{1}, a_{2}, \cdots, a_{n}, \cdots$ is defined by the following equation:
$$
a_{n+1}=2^{n}-3a_{n}, \quad n=0,1,2, \cdots
$$

(1) Find the expression of $a_{n}$ dependent on $a_{0}$ and $n$.

(2) Find $a_{0}$ such that for any positive integer $n$, $a_{n+1}>a_{n}$.

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