
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
The quadratic function $f(x) = ax^2 + bx + c$ ($a, b \in \mathbb{R}, a \neq 0$) satisfies the conditions:  
① When $x \in \mathbb{R}$, the graph of $f(x)$ is symmetric about the line $x = -1$; ② $f(1) = 1$; ③ The minimum value of $f(x)$ on $\mathbb{R}$ is 0;  
(1) Find the expression of the function $f(x)$;  
(2) Find the largest $m$ ($m > 1$), such that there exists $t \in \mathbb{R}$, as long as $x \in [1, m]$, then $f(x + t) \leq x$.

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