
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 a quadratic function $f(x)=ax^{2}+bx+c$ where $a,b \in R, a\neq 0$, it satisfies the following conditions:
1. When $x \in R$, the graph of $f(x)$ is symmetrical about the line $x=-1$.
2. $f(1)=1$.
3. The minimum value of $f(x)$ in $R$ is $0$.
(1) Find the analytical expression of the function $f(x)$.
(2) Find the largest $m(m > 1)$ such that there exists $t \in R$ so that for any $x \in [1,m]$, it satisfies $f(x+t)\leqslant x$.

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