Navigate with query params in remix-run/react router

I'm useing the new data Apis createBrowserRouter. I'm using it like this:

router.tsx

import { createBrowserRouter } from 'react-router-dom';
import { allRoutes } from './allRouts.tsx';
import type { Router } from '@remix-run/router/dist/router';

export const router: Router = createBrowserRouter(allRoutes);

Then in another router action file I use the router navigate function:

routerAction.tsx

export const routerAction = async ( 
    value: string | number
): Promise<void> => { 
            return router.navigate(value.toString());
    }
};

From what I could read in the type documentation (could not find information on the router instance on the site):

A Router instance manages all navigation and data loading/mutations

The question is how could I use this router to navigate with search parameters like I would with useSearchParams?

The router.navigate function has the following signature

/**
 * Navigate to the given path
 * @param to Path to navigate to
 * @param opts Navigation options (method, submission, etc.)
 */
navigate(to: To | null, opts?: RouterNavigateOptions): Promise<void>;

It takes a to prop that is of type To

/**
 * Describes a location that is the destination of some navigation, either via
 * `history.push` or `history.replace`. This may be either a URL or the pieces
 * of a URL path.
 */
export type To = string | Partial<Path>;

Which is either a path string or a partial Path object

/**
 * The pathname, search, and hash values of a URL.
 */
export interface Path {
  /**
   * A URL pathname, beginning with a /.
   */
  pathname: string;

  /**
   * A URL search string, beginning with a ?.
   */
  search: string;

  /**
   * A URL fragment identifier, beginning with a #.
   */
  hash: string;
}

You can use the Path object parameter to specify the target pathname and search parameters.

Example:

export const routerAction = async ( 
  value: string | number
): Promise<void> => { 
  return router.navigate({
    pathname: value.toString(),
    search: /* stringified search params, i.e. "?foo=bar" */,
  });
};