
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
Find $c$ such that $\lfloor c \rfloor$ satisfies:
\[ 2x^2 + 14x - 48 = 0 \]
and $\{ c \} = c - \lfloor c \rfloor$ satisfies:
\[ 9x^2 - 25x + 6 = 0. \]

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