
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 function $$f(x)= \begin{cases} cx+1 & \text{for } x<c \\ 3x^{4}+x^{2}c & \text{for } c\leq x<1\end{cases}$$ satisfies $$f(c^{2})= \frac {9}{8}$$;  
(1) Find the value of the constant $c$;  
(2) Solve the inequality $f(x)<2$.

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