
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 $f(x)=a\cos x+be^{x}$, where $a, b \in \mathbb{R}$, the tangent line of the curve $y=f(x)$ at the point $(0,f(0))$ is $y=-x$. Find the values of real numbers $a$ and $b$. Additionally, for $x \in [-\frac{\pi}{2}, +\infty)$, if $f(x) \leqslant c$ for all $x$, where $c \in \mathbb{Z}$, find the minimum value of $c$.

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