
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 $f(x) = x^3 + bx^2 + cx + d$, whose graph passes through point $P(0, 2)$, and the tangent line equation at point $M(-1, f(-1))$ is $6x - y + 7 = 0$.
(1) Find the analytical expression of function $y = f(x)$;
(2) Find the monotonic intervals of function $y = f(x)$.

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