
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 the sequences $\{a_n\}$ and $\{b_n\}$ with the general terms $$a_{n}= \frac {an^{2}+3}{bn^{2}-2n+2}$$ and $$b_{n}=b-a\left( \frac {1}{3}\right)^{n-1}$$ respectively, where $a$ and $b$ are real constants. If $$\lim_{n \to \infty}a_{n}=3$$ and $$\lim_{n \to \infty}b_{n}=- \frac {1}{4}$$, and $a$, $b$, $c$ form an arithmetic sequence, then the value of $c$ is \_\_\_\_\_.

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