
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
Let $a > 1$, and the function $f(x) = \log_{2}(x^{2} + 2x + a)$, where $x \in [-3, 3]$.

(1) Determine the intervals of monotonicity for the function $f(x)$.

(2) If the maximum value of $f(x)$ is 5, find the minimum value of $f(x)$.

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